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arXiv · 2609.13116

The zero set of the Zak transform of B-splines with applications to Gabor frames

Marzieh Hasannasab·Jakob Lemvig
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Abstract

We study the zero sets of the Zak transform $Z_λB_n(x,ν)$ of B-splines for $λ> 0$. Specifically, we provide a full characterization of the zero set for the hat spline for all positive values of the parameter $λ$ and for higher order B-splines when $λ> 1$. Finally, we apply these results to establish the frame property of integer-oversampled Gabor systems generated by B-splines. In particular, we characterize the frame property for integer-oversampled Gabor systems generated by the hat splines.

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Marzieh Hasannasab, Jakob Lemvig. 2026-09-11. The zero set of the Zak transform of B-splines with applications to Gabor frames. https://arxiv.org/abs/2609.13116

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